Abstract
Using an extension of the Boltzmann equation for the Wigner distribution appropriate for dilute spin 1 systems, spin diffusion equations are derived in the limit of large nuclear polarization in the non-degenerate régime. As an example of a system to which this work may be applied, the domain of validity of the Boltzmann equation for doubly spin-polarized deuterium, D↓↓, is studied. The effect of a finite field gradient is discussed. A calculated spin wave spectrum for a model one-dimensional system in the presence of a gradient is presented. Analogous effects in spin 1/2 systems are compared and contrasted.
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B. W. Statt and A. J. Berlinsky,Phys. Rev. Lett. 45, 2105, 1980.
M. W. Reynolds, M. E. Hayden, and M. N. Hardy,J. Low Temp. Phys. 84, 87, 1991.
I. Shinkoda, M. W. Reynolds, R. W. Cline, and W. N. Hardy,Phys. Rev. Lett. 57, 1243, 1986.
S. J. Buckle,Journal of Physics C: Solid State Physics 19, 3105, 1986.
N. P. Bigelow,Spin Wave Spectroscopy of Atomic Hydrogen Gas, Ph.D. Thesis (Cornell University, Ithaca, New York, 1990).
C. Lhuillier and F. Laloë,Journal de Physique 43, 225, 1982.
V. P. Silin,Zh. Eksp. Teor. Phys. 33, 1227, 1957.
C. Lhuillier and F. Laloë,Journal de Physique 43, 197, 1982.
E. M. Lifshitz and L. P. Pitaevskii,Statistical Physics: Part 2, pp. 19–20 (Pergamon, Oxford, 1980).
C. Lhuillier,J. Physique 44, 1–12, 1983. C. Lhuillier has also computed the D↓↓ spin transport coefficients based on the D-D inter-atomic potential.
R. L. Liboff,Introduction to the Theory of Kinetic Equations, Ch. 4 (Krieger, Melbourne, Florida, 1979), corrected reprint.
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions, Ch. 10 (Dover, New York, 1972).
J. H. Freed,Annales de Physique 10, 901, 1985.
B. R. Johnson, J. S. Denker, N. P. Bigelow, L. P. Lévy, J. H. Freed, and D. M. Lee,Phys. Rev. Lett. 52, 1508, 1984.
Claude Itzykson and Jean-Bernard Zuber,Quantum Field Theory (McGraw-Hill, New York, 1980), pp. 516–517.
H. J. Lipkin,Lie Groups for Pedestrians, Ch. 4 (North-Holland, Amsterdam, 1966).
R. N. Cahn,Semi-Simple Lie Algebras and Their Representations, Ch. 2 (Benjamin-Cummings, Menlo Park, California, 1984).
K. J. Heuvers,Lin. Alg. and Its Applic. 6, 83, 1973.
I. N. Stewart and D. O. Tall,Complex Analysis (Cambridge, 1983), p. 109.
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1972), pp. 448–450.
C. M. Bender and S. A. Orszag,Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), pp 569–570.
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1972), p. 478. For large values of λ n , the asymptotic form for the Airy integral on p. 449 may be used.
C. M. Bender and S. A. Orszag,Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), p. 541.
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This article appears in expanded from in K. A. Earle, Ph.D. thesis, Cornell University (1992).
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Earle, K.A., Freed, J.H. & Lee, D.M. Spin diffusion in doubly spin polarized atomic deuterium. J Low Temp Phys 89, 911–937 (1992). https://doi.org/10.1007/BF00683894
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DOI: https://doi.org/10.1007/BF00683894